(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 4.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 683497, 20586]*) (*NotebookOutlinePosition[ 694357, 20888]*) (* CellTagsIndexPosition[ 694061, 20874]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ StyleBox["Neural Networks", FontSlant->"Italic"], " Examples" }], "Title"], Cell[CellGroupData[{ Cell["Classification of Paper Quality", "Section", CellTags->{"b:1.1.0", "c:2", "i:3"}], Cell[CellGroupData[{ Cell["Introduction", "Subsection", CellMargins->{{54, Inherited}, {Inherited, Inherited}}], Cell["\<\ In this example different neural classifiers are compared using data from a \ hybrid gas array sensor, an electronic nose. The odors from five different \ cardboard papers from commercial manufacturers are recorded with the \ electronic nose. Different kinds of classifiers are trained to determine the \ origin of an unknown sample. \ \>", "Text", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"], Cell[TextData[{ "The data was kindly contributed by the Swedish Sensor Centre, S-SENCE, ", ButtonBox["www.ifm.liu.se/Applphys/S-SENCE", ButtonData:>{ URL[ "http://www.ifm.liu.se/Applphys/S-SENCE/"], None}, ButtonStyle->"Hyperlink"], ". More info", ButtonBox["rmation on the d"], "ata set can be found in \[OpenCurlyDoubleQuote]", StyleBox["Identification of Paper Quality Using a Hybrid Electronic Nose", CellMargins->{{54, Inherited}, {Inherited, Inherited}}], "\[CloseCurlyDoubleQuote] by Martin Holmberg, Fredrik Winquist, Ingemar \ Lundstr\[ODoubleDot]m, Julian W. Gardner, and Evor L. Hines,", StyleBox[" Sensors and Actuators B", FontSlant->"Italic"], " 26-27 (1995) 246-249." }], "Text", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"], Cell[TextData[{ "Load the ", StyleBox["Neural Networks", FontSlant->"Italic"], " package and the data." }], "MathCaption", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"], Cell[BoxData[ \(<< NeuralNetworks`\)], "Input", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"], Cell[BoxData[ \(\(<< paper.dat;\)\)], "Input", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"], Cell[TextData[{ "There is one data set for estimation, ", StyleBox["xs", FontSlant->"Italic"], " and ", StyleBox["ys", FontSlant->"Italic"], ", and one for validation of the classifiers, ", StyleBox["xv", FontSlant->"Italic"], " and ", StyleBox["yv", FontSlant->"Italic"], "." }], "Text", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"], Cell["Check the dimensions of the data.", "MathCaption", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"], Cell[CellGroupData[{ Cell[BoxData[{ \(Dimensions[xs]\), "\n", \(Dimensions[ys]\)}], "Input", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"], Cell[BoxData[ \({48, 15}\)], "Output", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"], Cell[BoxData[ \({48, 6}\)], "Output", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"] }, Open ]], Cell[TextData[{ "There are 48 data samples available for estimation. Each paper sample is \ characterized by 15 ", StyleBox["x ", FontSlant->"Italic"], "values from the 15 sensors in the electronic nose sensor array." }], "Text", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"], Cell[TextData[{ "Five different types of cardboard paper and plain air are measured, making \ six possible output classes. The correct class of each data sample is stored \ in ", StyleBox["y", FontSlant->"Italic"], ", with a 1 in the appropriate column indicating the class of the sample." }], "Text", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"], Cell["Check the class of the 27th sample of validation data.", "MathCaption", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"], Cell[CellGroupData[{ Cell[BoxData[ \(yv[\([27]\)]\)], "Input", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"], Cell[BoxData[ \({0, 0, 1, 0, 0, 0}\)], "Output", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"] }, Open ]], Cell["The 27th sample belongs to class 3.", "Text", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.0"], Cell["\<\ It is always a good idea to check how many data samples there are from each \ class.\ \>", "Text", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, 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0`0000=oo`0000000`000goo00@007ooOomoo`<00003Ool0000000Qoo`<000=oo`03001oogoo00=o o`<0009oo`@0009oo`@000=oo`8000=oo`@000=oo`8000Aoo`8000Aoo`<000Uoo`<000=oo`<00003 Ool0000000<000=oo`<000Qoo`001Woo00@007ooOol0021oo`03001oogoo00Aoo`03001oogoo00Yo o`03001oogoo035oo`03001oogoo00Aoo`03001oogoo01Eoo`03001oogoo01]oo`03001oogoo015o o`03001oogoo00Uoo`03001oogoo00Ioo`03001oogoo00moo`001goo0`009Woo0P003Goo00<007oo Ool00Woo00<007ooOol0Yoo`00\ \>"], ImageRangeCache->{{{0, 233.5}, {941, 0}} -> {-0.0320748, -0.100452, \ 0.00455739, 0.00455739}, {{7, 226.438}, {918.938, 783.313}} -> {-3.55412, \ -15.8807, 0.0851353, 0.328725}, {{7, 226.438}, {769.75, 634.125}} -> \ {-3.55412, -33.7597, 0.0851353, 0.170938}, {{7, 226.438}, {620.563, 485}} -> \ {-3.82926, -79.2074, 0.0868292, 0.227981}, {{7, 226.438}, {471.438, 335.813}} -> \ {-3.55412, -52.1554, 0.0851353, 0.105192}, {{7, 226.438}, {322.25, 186.625}} -> \ {-3.55412, -50.8866, 0.0851353, 0.0788943}, {{7, 226.438}, {173.063, \ 37.4375}} -> {-3.55412, -62.6567, 0.0851353, 0.0788943}}, CellTags->"b:1.1.1"] }, Open ]], Cell["The dashed lines indicate incorrectly classified data.", "Text", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.1"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[ButtonBox["Radial Basis Function Network", ButtonData:>{"NeuralNetworks 6.0.0", "TAG"}, ButtonStyle->"AddOnsLinkText"]], "Subsection", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->{"b:1.1.2", "c:4"}], Cell[TextData[{ "A ", ButtonBox["radial basis function (RBF) network", ButtonData:>{"NeuralNetworks 6.0.0", "TAG"}, ButtonStyle->"AddOnsLinkText"], " will be used on the cardboard paper data. RBF networks are often not \ suitable for use in high-dimensional problems like this one, which has 15 \ input dimensions. It is, however, possible to choose to use only a subset of \ the inputs. Choosing a subset of inputs can be seen as a simple form of \ feature extraction. To simplify the problem, only three inputs will be used \ and only two of the paper types will be classified. 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Because the radial basis \ functions have local support where they are nonzero, the training often gets \ trapped in poor local minima. Quite frequently, one of the classes will be \ totally misclassified. You will see this if you reevaluate the example with a \ different initialization of the RBF network. Correct classification is \ obtained when there is one basis function at each class center. If any of the \ class centers has not managed to attract a basis function during the \ training, then this class will not be correctly classified.\ \>", "Text", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.2"] }, Open ]], Cell[CellGroupData[{ Cell["Feedforward Network", "Subsection", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->{"b:1.1.3", "c:5"}], Cell[TextData[{ "Now try a ", ButtonBox["feedforward neural network", ButtonData:>{"NeuralNetworks 5.0.0", "TAG"}, ButtonStyle->"AddOnsLinkText"], ". As for RBF networks, a sigmoidal nonlinearity is added to the output so \ that the outputs are constrained to the interval 0 to 1. The result will vary \ each time the commands are evaluated due to the random nature of the \ initialization and training processes." }], "Text", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.3"], Cell[TextData[{ "Load the ", StyleBox["Mathematica", FontSlant->"Italic"], " ", StyleBox["application package ", CellMargins->{{54, Inherited}, {Inherited, Inherited}}], StyleBox["Neural Networks", FontSlant->"Italic"], " and the data." }], "MathCaption", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.3"], Cell[BoxData[{ \(<< NeuralNetworks`\), "\n", \(<< LinearAlgebra`MatrixManipulation`\)}], "Input", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.3"], Cell[BoxData[ \(\(<< paper.dat;\)\)], "Input", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.3"], Cell["Initialize a feedforward network without any hidden neurons.", \ "MathCaption", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, 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\(fdfrwrd2[xv[\([27]\)]]\)], "Input", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.3"], Cell[BoxData[ \({0.1123883590657711`, 1.5807526374065728`*^-11, 0.9999999534007791`, 1.593046637972903`*^-7, 0.00004942216025209225`, 0.00017779504902184522`}\)], "Output", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.3"] }, Open ]], Cell[TextData[{ "A crisp classification is obtained by setting all output values greater \ than 0.5 to ", StyleBox["True", "MR"], StyleBox[".", "MR", FontFamily->"Times New Roman"] }], "MathCaption", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.3"], Cell[CellGroupData[{ Cell[BoxData[ \(Map[# > 0.5 &, fdfrwrd2[xv[\([27]\)]]]\)], "Input", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.3"], Cell[BoxData[ \({False, False, True, False, False, False}\)], "Output", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.3"] }, Open ]], Cell["The 27th 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For example, you can introduce a layer of hidden neurons. \ \>", "Text", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.3"], Cell[TextData[StyleBox["Three types of neural networks have been used to \ classify the paper quality data: VQ, RBF, and feedforward. What conclusion \ can you draw from the comparison?\nAs mentioned before, RBF networks often \ have problems with local minima, especially if the dimension of the input \ space is high. To reduce this problem, only three of the available 15 \ dimensions were used. Of course, when 12 dimensions are neglected, there is a \ danger that the remaining three dimensions do not contain enough information \ to separate the classes. Hence, RBF networks are not very good for this \ problem.\nA feedforward network also may have problems with local minima, \ especially if you change the network and include a hidden layer, but these \ problems are not as severe as they are for the RBF network. You can test for \ problems by reevaluating the example a few times. Though the VQ network does \ not have any problems with local minima in this example, it may with other \ data. It is hard to say which classifier is the best, but the VQ network was \ the easiest one to train.", CellMargins->{{54, Inherited}, {Inherited, Inherited}}]], "Text", CellMargins->{{54, Inherited}, {Inherited, Inherited}}, CellTags->"b:1.1.3"] }, Open ]] }, Open ]] }, FrontEndVersion->"4.2 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 685}}, ScreenStyleEnvironment->"AllBrackets", WindowToolbars->{}, WindowSize->{1014, 651}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, CellLabelAutoDelete->True, Magnification->1, StyleDefinitions -> "Classroom.nb" ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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